A phenomenological cohesive model for the macroscopic simulation of cell-matrix adhesions

A multi-scale clutch model for adhesion complex mechanics

Cell-matrix adhesion is a central mechanical function to a large number of phenomena in physiology and disease, including morphogenesis, wound healing, and tumor cell invasion. Today, how single cells respond to different extracellular cues has been comprehensively studied. However, how the mechanical behavior of the main individual molecules that form an adhesion complex cooperatively responds to force within the adhesion complex is still poorly understood. This is a key aspect of cell adhesion because how these cell adhesion molecules respond to force determines not only cell adhesion behavior but, ultimately, cell function. To answer this question, we develop a multi-scale computational model for adhesion complexes mechanics. We extend the classical clutch hypothesis to model individual adhesion chains made of a contractile actin network, a talin rod, and an integrin molecule that binds at individual adhesion sites on the extracellular matrix. We explore several scenarios of integrins dynamics and analyze the effects of diverse extracellular matrices on the behavior of the adhesion molecules and on the whole adhesion complex. Our results describe how every single component of the adhesion chain mechanically responds to the contractile actomyosin force and show how they control the traction forces exerted by the cell on the extracellular space. Importantly, our computational results agree with previous experimental data at the molecular and cellular levels. Our multi-scale clutch model presents a step forward not only to further understand adhesion complexes mechanics but also to impact, e.g., the engineering of biomimetic materials, tissue repairment, or strategies to arrest tumor progression.

Elasticity-associated rebinding rate of molecular bonds between soft elastic media

A quantitative understanding of how cells interact with their extracellular matrix via molecular bonds is fundamental for many important processes in cell biology and engineering. In these interactions, the deformability of cells and matrix are usually comparable with that of the bonds, making their rebinding events globally coupled with the deformation states of whole systems. Unfortunately, this important principle is not realized or adopted in most conventional theoretical models for analyzing cellular adhesions. In this study, we considered a new theoretical model of a cluster of ligand-receptor bonds between two soft elastic bodies, in which the rebinding rates of ligands to receptors are described, by considering the deformation of the overall system under the influence of bond distributions. On the basis of theory of continuum mechanics and statistical mechanics, we obtained an elasticity-associated rebinding rate of open bonds in a closed analytical form that highly depends on the binding states and distributions of all other bonds, as well as on the overall deformation energy stored in the elastic bodies and all closed bonds. On the basis of this elasticity-associated rebinding rate and by performing Monte Carlo simulations, we uncovered new mechanisms underlying the adhesion stability of molecular bond clusters associated with deformable elastic bodies. Moreover, we revealed that the rebinding processes of molecular bonds is not only dependent on interfacial separation but is related to overall energy. This newly proposed rebinding rate may substantially improve our understanding of how cells adapt to their microenvironments by adjusting their mechanical properties through cytoskeleton remodeling.

Breast Cancer Cells Adapt Contractile Forces to Overcome Steric Hindrance

Cell migration through the extracellular matrix is governed by the interplay between cell-generated propulsion forces, adhesion forces, and resisting forces arising from the steric hindrance of the matrix. Steric hindrance in turn depends on matrix porosity, matrix deformability, cell size, and cell deformability. In this study, we investigate how cells respond to changes in steric hindrance that arise from altered cell mechanical properties. Specifically, we measure traction forces, cell morphology, and invasiveness of MDA-MB 231 breast cancer cells in three-dimensional collagen gels. To modulate cell mechanical properties, we either decrease nuclear deformability by twofold overexpression of the nuclear protein lamin A or we introduce into the cells stiff polystyrene beads with a diameter larger than the average matrix pore size. Despite this increase of steric hindrance, we find that cell invasion is only marginally inhibited, as measured by the fraction of motile cells and the mean invasion depth. To compensate for increased steric hindrance, cells employ two alternative strategies. Cells with higher nuclear stiffness increase their force polarity, whereas cells with large beads increase their net contractility. Under both conditions, the collagen matrix surrounding the cells stiffens dramatically and carries increased strain energy, suggesting that increased force polarity and increased net contractility are functionally equivalent strategies for overcoming an increased steric hindrance.